Time-Series Forecasting based on Cumulative Data (TSFCD) is a crucial problem
in decision-making across various industrial scenarios. However, existing
time-series forecasting methods often overlook two important characteristics of
cumulative data, namely monotonicity and irregularity, which limit their
practical applicability. To address this limitation, we propose a principled
approach called Monotonic neural Ordinary Differential Equation (MODE) within
the framework of neural ordinary differential equations. By leveraging MODE, we
are able to effectively capture and represent the monotonicity and irregularity
in practical cumulative data. Through extensive experiments conducted in a
bonus allocation scenario, we demonstrate that MODE outperforms
state-of-the-art methods, showcasing its ability to handle both monotonicity
and irregularity in cumulative data and delivering superior forecasting
performance.

基于神经常微分方程模型的模态（MODE）可有效地捕捉和表示实际累积数据中的单调性和不规则性，并展现出卓越的预测性能。

单调神经常微分方程：累积数据的时间序列预测

Monotonic Neural Ordinary Differential Equation: Time-series Forecasting  for Cumulative Data

Health conditions among patients in intensive care units (ICUs) are monitored
via electronic health records (EHRs), composed of numerical time series and
lengthy clinical note sequences, both taken at irregular time intervals.
Dealing with such irregularity in every modality, and integrating irregularity
into multimodal representations to improve medical predictions, is a
challenging problem. In this paper, we address this problem by (1) modeling
irregular time series by incorporating hand-crafted imputation embeddings into
learned interpolation embeddings via a gating mechanism; (2) casting a series
of clinical note representations as multivariate irregular time series and
tackling irregularity via a time attention mechanism; and (3) fusing
multimodalities with an interleaved attention mechanism across temporal steps
to integrate irregularity into multimodal representations. To the best of our
knowledge, this is the first work to thoroughly model irregularity in
multimodalities and to take into account temporal knowledge in multimodal
fusion, for improving medical predictions. The results on two medical
prediction tasks show that our proposed methods outperform the state-of-the-art
(SOTA) methods in both every single modality and multimodal fusion scenarios,
illustrating the effectiveness of our methods and the value of modeling
irregularity in multimodal fusion.

本论文通过手工建模和学习内插嵌入，采用分离机制建模不规则的时间序列；采用时间注意力机制，将临床记录的一系列表示为多元不规则时间序列，并采用交织注意机制跨时间步骤进行多模态融合，以整合多模态表示。结果表明，我们提出的方法在单一模态和多模态情景下都优于现有方法，说明了我们方法的有效性和模拟不规则性的价值。